Hi. How to prove that equation:

Additional informations:

and are heights of acute-angled triangle .

Illustration: http://i.imgur.com/9O8Bm.jpg

I would really appreciate any help. http://www.mymathforum.com/images/sm...on_biggrin.gif

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- Oct 25th 2012, 11:22 AMOgniokProve the following equation
Hi. How to prove that equation:

Additional informations:

and are heights of acute-angled triangle .

Illustration: http://i.imgur.com/9O8Bm.jpg

I would really appreciate any help. http://www.mymathforum.com/images/sm...on_biggrin.gif - Oct 25th 2012, 03:05 PMBobPRe: Prove the following equation
First point is that most of the diagram is unnecessary.

If you don't need or

If you don't need or

Further, and serve no purpose.

All that you need is the triangle and the perpendiculars and

Using Pythagoras twice, with the triangles and

Now repeat that sequence using the triangles and

Having done that, add the resulting equation to the one that's just been derived. - Oct 26th 2012, 07:29 AMOgniokRe: Prove the following equation
Thank you very much. :D I've finally done that :D

Here are full calculations:

- Nov 1st 2012, 03:02 AMelisaevedentRe: Prove the following equation